UVA 10991 / Geometry - Cosine rule

/***
 created: 2022-06-17-23.34.25
***/

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
template<typename U> using ordered_set=tree<U, null_type,less<U>,rb_tree_tag,tree_order_statistics_node_update>;
#define ll long long
#define test int tt; cin>>tt; for(int cs=1;cs<=tt;cs++)
#define get_lost_idiot return 0
#define nl '\n'

int main()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);

    test
    {
        double r1,r2,r3;

        cin>>r1>>r2>>r3;

        double a=r1+r2;

        double b=r2+r3;

        double c=r1+r3;

        double s=(a+b+c)/2.00;

        double trainglearea = sqrt(s*(s-a)*(s-b)*(s-c));

        double angle1 = acos(((b*b)+(c*c)-(a*a))/2.0/b/c);

        double sector1= (angle1*r3*r3) /2.00 ;

        double angle2 = acos(((a*a)+(c*c)-(b*b))/2.00/a/c);

        double sector2 = (angle2*r1*r1) /2.00 ;

        double angle3 = acos(((a*a)+(b*b)-(c*c))/2.00/a/b);

        double sector3 = (angle3*r2*r2) /2.00 ;

        double ans = trainglearea - sector1 - sector2 - sector3;

        cout<<fixed<<setprecision(6)<<ans<<nl;
    }



    get_lost_idiot;
}